In section 4-1, you will be reviewing how to classify triangles by their sides and angles and how to find angle measures in triangles. To look back at the textbook for more review, you can go to pages 194-201.
Vocabulary:Triangle - a plane figure with 3 sides and 3 anglesVertex - each of the 3 points joining the sides of a triangleAdjacent sides - 2 sides sharing a common vertexLegs - the 2 sides of a right triangle or an isosceles triangleBase - the third side of an isosceles triangle Hypotenuse - the opposite side of the right triangleInterior angles - angles that are in between the 2 linesExterior angles - angles that are on the outside of the 2 linesCorollary - acute angles of a right angle; a proof that is easily proven.Theorems: Triangle Sum Thm - the sum of the measures of the interior angles of a triangle is 180° Exterior Angle Thm - created when the sides of a triangle are extended. Each exterior angle is adjacent to one interior angle. (in the diagram, <1 is an exterior angle.) Exterior angles and adjacent interior angles form a linear pair. Corollary to the Triangle Sum Thm - the acute angles of a right triangle are complementary.
Sample Problems 1) find x
By using the exterior angle theorem, you can say:
x = 35 + 100 x = 135
2) find x
By using the Triangle Sum Thm, you can do:
35 + 23 + b = 180
58 + b = 180
b = 122
And by the Vertical Angles Theorem, you can that angle A = 122.
Therefore, being able to use the Triangle Sum Theorem to do:
27 + 22 + x = 180
149 + x = 180 x = 31
3) Given: êABC Prove: m<1+m<2+m<3=180
PRACTICE!
1) Solve the following proof 2) Find the measure of the exterior angle 3) Find the measure of the angles with a red number in them. 4) Find the measure of angle LNM in this triangle.
In section 4-1, you will be reviewing how to classify triangles by their sides and angles and how to find angle measures in triangles. To look back at the textbook for more review, you can go to pages 194-201.
Helpful Websites:
http://www.winpossible.com/lessons/Geometry_Triangle_Angle-Sum_Theorem.html
http://www.cliffsnotes.com/study_guide/Exterior-Angle-of-a-Triangle.topicArticleId-18851,articleId-18784.html
Vocabulary:Triangle - a plane figure with 3 sides and 3 anglesVertex - each of the 3 points joining the sides of a triangleAdjacent sides - 2 sides sharing a common vertexLegs - the 2 sides of a right triangle or an isosceles triangleBase - the third side of an isosceles triangle
Hypotenuse - the opposite side of the right triangle
Triangle Sum Thm - the sum of the measures of the interior angles of a triangle is 180°
Exterior Angle Thm - created when the sides of a triangle are extended. Each exterior angle is adjacent to one interior angle. (in the diagram, <1 is an exterior angle.) Exterior angles and adjacent interior angles form a linear pair.
Corollary to the Triangle Sum Thm - the acute angles of a right triangle are complementary.
Sample Problems
1) find x
By using the exterior angle theorem, you can say:
x = 35 + 100
x = 135
2) find x
By using the Triangle Sum Thm, you can do:
35 + 23 + b = 180
58 + b = 180
b = 122
And by the Vertical Angles Theorem, you can that angle A = 122.
Therefore, being able to use the Triangle Sum Theorem to do:
27 + 22 + x = 180
149 + x = 180
x = 31
3) Given: êABC
Prove: m<1+m<2+m<3=180
PRACTICE!
1) Solve the following proof
2) Find the measure of the exterior angle
3) Find the measure of the angles with a red number in them.
4) Find the measure of angle LNM in this triangle.